Method for determining a corrected wheel radius on the basis of the measured yaw rate

ABSTRACT

A method for determining a wheel radius of a motor vehicle, including calculating a yaw rate of the motor vehicle by means of a wheel speed of at least one wheel and a predefined wheel radius. The calculated yaw rate is compared with a measured yaw rate. The wheel speed is adapted. The calculation of the yaw rate is input, of the at least one wheel by means of a correction factor, so that the calculated yaw rate is equal to the measured yaw rate. The correction factor and the predefined wheel radius or the wheel speed is multiplied. The calculation of the yaw rate is input, for the determination of a corrected wheel radius or of a corrected wheel speed.

The present invention relates to a method for determining a wheel radius having the features of the preamble of claim 1, to a device for a motor vehicle for determining a wheel radius and to a steer-by-wire steering system having such a device.

The diameter, circumference and radius of a vehicle wheel or tire is necessary to determine a large number of vehicle variables. These include, for example, the wheel speed, the vehicle speed, the distance travelled, the current position of the vehicle or the orientation of the vehicle. The variables specified above are in turn decisive for vehicle systems, such as for example the antilock brake system (ABS), the traction control system (ASR) or the electronic stability program (ESP).

The wheel circumference of a vehicle wheel is defined by the rolling circumference, that is to say the distance which is travelled per revolution of the wheel. The wheel rolling circumferences of each vehicle wheel are not constant and can change, for example, for the following reasons: air pressure fluctuations, fabrication tolerances of the wheels, changes in temperature, wear or changing of the wheel.

German laid-open patent application EP 1 826 530 A1 discloses a method for determining a wheel circumference. This solution proves disadvantageous in that to determine the wheel circumference it is firstly necessary to travel straight ahead for a certain period of time and additionally cornering is also necessary.

The object of the present invention is therefore to disclose an improved method and an improved device for determining a radius of a motor vehicle wheel.

This object is achieved by a method for determining a wheel radius having the features of claim 1 and a device for determining a wheel radius for motor vehicles as well as a steer-by-wire steering system having the device. Advantageous developments of the invention are specified in the dependent claims. Advantageous developments arise from the dependent claims.

Accordingly, a method for determining a wheel radius of a motor vehicle is provided which has the following steps:

-   -   calculating a yaw rate of the motor vehicle by means of a wheel         speed of at least one wheel and a predefined wheel radius,     -   comparing the calculated yaw rate with a measured yaw rate,     -   adapting the wheel speed, input in the calculation of the yaw         rate, of the at least one wheel by means of a correction factor         so that the calculated yaw rate is equal to the measured yaw         rate,     -   multiplying the correction factor and the predefined wheel         radius and/or the wheel speed, input in the calculation of the         yaw rate, for the determination of a corrected wheel radius         and/or of a corrected wheel speed.

The method permits the actual wheel radii to be determined easily by determining a respective correction factor.

The determination of the correction factor is preferably carried out for all four wheels. A individual correction factor is therefore obtained for each wheel.

In one preferred embodiment, only the front wheels are steerable. For this case, the correction factors are calculated with the following formula:

${k_{RR} = {{\frac{{b \cdot \overset{.}{\psi}} - {{k_{FL} \cdot v_{FL} \cdot \cos}\;\delta_{FL}}}{- v_{RR}}\mspace{14mu}{with}\mspace{14mu} k_{FL}} = \frac{\overset{.}{\psi} \cdot l}{{v_{FL} \cdot \sin}\;\delta_{FL}}}},{k_{RL} = {{\frac{{b \cdot \overset{.}{\psi}} + {{k_{FR} \cdot v_{FR} \cdot \cos}\;\delta_{FR}}}{v_{RL}}\mspace{14mu}{with}\mspace{14mu} k_{FR}} = \frac{\overset{.}{\psi} \cdot l}{{v_{FR} \cdot \sin}\;\delta_{FR}}}},$

where

-   -   ν_(FL) Wheel speed front left     -   ν_(FR) Wheel speed front right     -   ν_(RL) Wheel speed rear left     -   ν_(RR) Wheel speed rear right     -   δ_(FL) Wheel steering angle front left     -   δ_(FR) Wheel steering angle front right     -   l Wheelbase     -   b Track width

In a further preferred embodiment, the respective correction factors are determined for each individual wheel of a rear wheel steering system. For this case, the correction factors are calculated with the following formula:

${k_{RR} = {{\frac{{{- b} \cdot \overset{.}{\psi}} + {\cos\;{\delta_{FL} \cdot \frac{\overset{.}{\psi}\left( {{{l \cdot \cos}\;\delta_{RR}} + {{b \cdot \sin}\;\delta_{RR}}} \right)}{\sin\left( {\delta_{RR} - \delta_{FL}} \right)}}}}{{v_{RR} \cdot \cos}\;\delta_{RR}}\mspace{14mu}{with}\mspace{14mu} k_{FL}} = \frac{\overset{.}{\psi} \cdot \left( {{{l \cdot \cos}\;\delta_{RR}} + {{b \cdot \sin}\;\delta_{RR}}} \right)}{v_{FL} \cdot {\sin\left( {\delta_{RR} - \delta_{FL}} \right)}}}},{k_{RL} = {{\frac{{b \cdot \overset{.}{\psi}} + {\cos\;{\delta_{FR} \cdot \frac{\overset{.}{\psi}\left( {{{l \cdot \cos}\;\delta_{RL}} + {{b \cdot \sin}\;\delta_{RL}}} \right)}{\sin\left( {\delta_{FR} - \delta_{RL}} \right)}}}}{{v_{RL} \cdot \cos}\;\delta_{RL}}\mspace{14mu}{with}\mspace{14mu} k_{FR}} = \frac{\overset{.}{\psi} \cdot \left( {{{l \cdot \cos}\;\delta_{RL}} + {{b \cdot \sin}\;\delta_{RL}}} \right)}{v_{FR} \cdot {\sin\left( {\delta_{FR} - \delta_{RL}} \right)}}}},$

where

-   -   δ_(RL) Wheel steering angle rear left     -   δ_(RR) Wheel steeling angle rear right.

The following measured values are preferably input in the calculation of the correction factors: the yaw rate and the steering wheel angle of the steerable wheels.

It is advantageous if the correction factors are determined only if the measured yaw rate is >0.05°/s and/or the measured yaw acceleration is <0.01°/s². In addition it is preferred that the wheel speed is >0.2 m/s and/or the wheel acceleration is <0.1 m/s².

Furthermore, a device is provided which is configured to carry out the method described above.

In addition, a steer-by-wire steering system is provided for a motor vehicle having this device. It is also conceivable and possible that the method can be used for an electromechanical motor vehicle steering system. It is also conceivable and possible to implement the method for an electromechanical brake, an electric drive or in a rear wheel steering system.

A preferred embodiment of the invention will be explained in more detail below with reference to the drawings. Identical or identically acting components are denoted by the same reference symbols in the figures.

In the drawings:

FIG. 1: shows a schematic illustration of a steer-by-wire steering system,

FIG. 2: shows a schematic plan view of a motor vehicle, and

FIG. 3: shows a block diagram of a calculation of a corrected wheel speed.

FIG. 1 shows a steer-by-wire steering system 1. A rotational angle sensor (not illustrated), which acquires the driver steering angle which is applied by rotation of a steering input means 3, which is embodied as a steering wheel in the example, is mounted on a steering shaft 2. However, it is also additionally possible to acquire a steering torque. Furthermore, a feedback actuator 4 is mounted on the steering shaft 2, said feedback actuator 4 serving to simulate the reactions from the roadway 60 on the steering wheel 3 and therefore to give the driver feedback about the steering and driving behavior of the vehicle. An electric steering actuator 5 controls the position of the steering wheel 6. The steering actuator 5 acts via a steering rack-steering gear 7, such as for example a toothed rack-steering gear, wherein the toothed rack 8 acts indirectly on the steering wheel 6 via ball joints (not illustrated) with track rods 9 and other components.

FIG. 2 illustrates the motor vehicle in a plan view. Provided on a front axle with respect to direction of travel are two steerable front wheels FL, FR which can be pivoted through wheel steering angles δ_(FL), δ_(FR). A rear axle has two further non-steerable wheels RL, RR which can be pivoted through wheel steering angles δ_(RL), δ_(RR). Each wheel FL, FR, RL, RR is assigned a wheel speed ν_(FL), ν_(FR), ν_(RL), ν_(RR). The axles have a wheelbase l. The vehicle has a track width b. The vehicle moves about the vertical axis 10 at an angular speed {dot over (ψ)}, the so-called yaw rate. The vertical axis 10 is here a vertical axis through the center of gravity of the vehicle about which the vehicle rotates during steering movements on its journey. The yaw rate {dot over (ψ)}, the wheel speeds ν_(FL), ν_(FR), ν_(RL), ν_(RR) and the wheel steering angles δ_(FL), δ_(FR), δ_(RL), δ_(RR) are measured and the actual, corrected radii of the vehicle wheels are determined therefrom.

FIG. 3 shows the determination of correction factors k_(RR), k_(FR), k_(RL), k_(RR) of the radii of the motor vehicle wheels FL, FR, RL, RR.

During the determination of the correction factors k_(RR), k_(FR), k_(RL), k_(RR), the validity range is preferably defined by the following conditions:

-   -   wheel acceleration a_(FL), a_(FR), a_(RL), a_(RR)<0.1 m/s²     -   wheel speed ν_(FL), ν_(FR), ν_(RL), ν_(RR)>0.2 m/s     -   yaw rate {dot over (ψ)}>0.05°/s     -   yaw acceleration {umlaut over (ψ)}<0.01°/s².

The vehicle must move with a relatively high yaw rate and with a relatively low speed so that the sideslip angle remains low. The variables in the equations have the following meaning:

-   -   ν_(FL) Wheel speed front left     -   ν_(FR) Wheel speed front right     -   ν_(RL) Wheel speed rear left     -   ν_(RR) Wheel speed rear right     -   δ_(FL) Wheel steering angle front left     -   δ_(FR) Wheel steering angle front right     -   l Wheelbase     -   b Track width     -   k_(FL) Correction factor front left     -   k_(FR) Correction factor front right     -   k_(RL) Correction factor rear left     -   k_(RR) Correction factor rear right     -   {dot over (ψ)} Measured yaw rate     -   {circumflex over ({dot over (ψ)})} Calculated yaw rate     -   ω Wheel speed     -   r_(FL) Wheel radius front left     -   r_(FR) Wheel radius front right     -   r_(RL) Wheel radius rear left     -   r_(RR) Wheel radius rear right

The yaw rate of the motor vehicle about the vertical axis can be calculated from any wheel speed with a defined wheel radius by taking into account the rigid body dynamics.

The wheel speed ω and a fixed wheel radius value r are used to calculate the wheel speeds in a first step 11.

The speeds of the steerable front wheels are obtained from

ν _(FL)=ν _(RR) +ω×r _(FL) ^(RR) ν _(FR)=ν _(RL) +ω×r _(FR) ^(RL).

The yaw rate of the motor vehicle can be calculated in a second step 12 by resolving the vector equations with a fixed wheel radius value in various ways:

${\begin{bmatrix} {{v_{FL} \cdot \cos}\;\delta_{FL}} \\ {{v_{FL} \cdot \sin}\;\delta_{FL}} \end{bmatrix} = {{\begin{bmatrix} v_{RR} \\ Ø \end{bmatrix} + \begin{bmatrix} i & j & k \\ 0 & 0 & \hat{\overset{.}{\psi}} \\ l & {- b} & \varnothing \end{bmatrix}} = \begin{bmatrix} {v_{RR} + {\hat{\overset{.}{\psi}} \cdot b}} \\ {\hat{\overset{.}{\psi}} \cdot l} \end{bmatrix}}},{\begin{bmatrix} {{v_{FR} \cdot \cos}\;\delta_{FR}} \\ {{v_{FR} \cdot \sin}\;\delta_{FR}} \end{bmatrix} = {{\begin{bmatrix} v_{RL} \\ Ø \end{bmatrix} + \begin{bmatrix} i & j & k \\ 0 & 0 & \hat{\overset{.}{\psi}} \\ l & b & \varnothing \end{bmatrix}} = \begin{bmatrix} {v_{RL} - {\hat{\overset{.}{\psi}} \cdot b}} \\ {\hat{\overset{.}{\psi}} \cdot l} \end{bmatrix}}},{\hat{\overset{.}{\psi}} = {{\frac{{v_{FL} \cdot \sin}\;\delta_{FL}}{l}\mspace{14mu}\hat{\overset{.}{\psi}}} = \frac{{v_{FL} \cdot \cos}\;\delta_{RR}}{b}}},{\hat{\overset{.}{\psi}} = \frac{{v_{FR} \cdot \sin}\;\delta_{FR}}{l}},{\hat{\overset{.}{\psi}} = {\frac{{{{- v_{FR}} \cdot \cos}\;\delta_{FR}} + v_{RL}}{b}.}}$

In addition to the calculated wheel speeds, the measured wheel steering angles of the two front wheels δ_(FL), δ_(FR) are used for this.

In a subsequent step 13, the calculated yaw rate values {circumflex over ({dot over (ψ)})} are compared with the measured yaw rate values. The calculated wheel speeds are corrected by multiplication by a correction factor in a further step 14, in such a way that the yaw rates which are calculated from the wheel speeds are equal to the measured yaw rate. Since the wheel speed is known, the correction factors correct the wheel radii.

The correction factors for the four wheels are therefore obtained from:

${k_{RR} = {{\frac{{b \cdot \overset{.}{\psi}} - {{k_{FL} \cdot v_{FL} \cdot \cos}\;\delta_{FL}}}{- v_{RR}}\mspace{14mu}{with}\mspace{14mu} k_{FL}} = \frac{\overset{.}{\psi} \cdot l}{{v_{FL} \cdot \sin}\;\delta_{FL}}}},{k_{RL} = {{\frac{{b \cdot \overset{.}{\psi}} + {{k_{FR} \cdot v_{FR} \cdot \cos}\;\delta_{FR}}}{v_{RL}}\mspace{14mu}{with}\mspace{14mu} k_{FR}} = {\frac{\overset{.}{\psi} \cdot l}{{v_{FR} \cdot \sin}\;\delta_{FR}}.}}}$

In a rear wheel steering system, the respective correction factors for each individual wheel are calculated with the following formula:

${k_{RR} = {{\frac{{{- b} \cdot \overset{.}{\psi}} + {\cos\;{\delta_{FL} \cdot \frac{\overset{.}{\psi}\left( {{{l \cdot \cos}\;\delta_{RR}} + {{b \cdot \sin}\;\delta_{RR}}} \right)}{\sin\left( {\delta_{RR} - \delta_{FL}} \right)}}}}{{v_{RR} \cdot \cos}\;\delta_{RR}}\mspace{14mu}{with}\mspace{14mu} k_{FL}} = \frac{\overset{.}{\psi} \cdot \left( {{{l \cdot \cos}\;\delta_{RR}} + {{b \cdot \sin}\;\delta_{RR}}} \right)}{v_{FL} \cdot {\sin\left( {\delta_{RR} - \delta_{FL}} \right)}}}},{k_{RL} = {{\frac{{b \cdot \overset{.}{\psi}} + {\cos\;{\delta_{FR} \cdot \frac{\overset{.}{\psi}\left( {{{l \cdot \cos}\;\delta_{RL}} + {{b \cdot \sin}\;\delta_{RL}}} \right)}{\sin\left( {\delta_{FR} - \delta_{RL}} \right)}}}}{{v_{RL} \cdot \cos}\;\delta_{RL}}\mspace{14mu}{with}\mspace{14mu} k_{FR}} = \frac{\overset{.}{\psi} \cdot \left( {{{l \cdot \cos}\;\delta_{RL}} + {{b \cdot \sin}\;\delta_{RL}}} \right)}{v_{FR} \cdot {\sin\left( {\delta_{FR} - \delta_{RL}} \right)}}}},$

where

-   -   δ_(RL) Wheel steering angle rear left     -   δ_(RR) Wheel steering angle rear right.

The corrected wheel speeds ν_(FL,corr), ν_(FR,cor), ν_(RL,corr), ν_(RR,corr) are subsequently input into the vehicle movement dynamics control systems 15. The corrected wheel radii can also be calculated by multiplication by the corresponding correction factor and used to determine further important vehicle variables, which can then in turn be input into driving assistance systems. 

1.-12. (canceled)
 13. A method for determining a wheel radius of a motor vehicle, comprising: calculating a yaw rate of the motor vehicle by a wheel speed of at least one wheel which is determined by a predefined wheel radius, comparing the calculated yaw rate to a measured yaw rate, adapting the wheel speed, input in the calculation of the yaw rate, of the at least one wheel by means of a correction factor so that the calculated yaw rate is equal to the measured yaw rate, and multiplying the correction factor and the predefined wheel radius and/or the wheel speed, input in the calculation of the yaw rate, for the determination of a corrected wheel radius and/or of a corrected wheel speed.
 14. The method of claim 13 wherein the determination of the correction factor is carried out for all four wheels of the motor vehicle.
 15. The method of claim 13 wherein front wheels of the motor vehicle are steerable.
 16. The method of claim 15 wherein the correction factors are calculated with the following formula: ${k_{RR} = {{\frac{{b \cdot \overset{.}{\psi}} - {{k_{FL} \cdot v_{FL} \cdot \cos}\;\delta_{FL}}}{- v_{RR}}\mspace{14mu}{with}\mspace{14mu} k_{FL}} = \frac{\overset{.}{\psi} \cdot l}{{v_{FL} \cdot \sin}\;\delta_{FL}}}},{k_{RL} = {{\frac{{b \cdot \overset{.}{\psi}} + {{k_{FR} \cdot v_{FR} \cdot \cos}\;\delta_{FR}}}{v_{RL}}\mspace{14mu}{with}\mspace{14mu} k_{FR}} = \frac{\overset{.}{\psi} \cdot l}{{v_{FR} \cdot \sin}\;\delta_{FR}}}},$ where ν_(FL) Wheel speed front left ν_(FR) Wheel speed front right ν_(RL) Wheel speed rear left ν_(RR) Wheel speed rear right δ_(FL) Wheel steering angle front left δ_(FR) Wheel steering angle front right l Wheelbase b Track width.
 17. The method of claim 15 wherein the correction factors are calculated with the following formula: ${k_{RR} = {{\frac{{{- b} \cdot \overset{.}{\psi}} + {\cos\;{\delta_{FL} \cdot \frac{\overset{.}{\psi}\left( {{{l \cdot \cos}\;\delta_{RR}} + {{b \cdot \sin}\;\delta_{RR}}} \right)}{\sin\left( {\delta_{RR} - \delta_{FL}} \right)}}}}{{v_{RR} \cdot \cos}\;\delta_{RR}}\mspace{14mu}{with}\mspace{14mu} k_{FL}} = \frac{\overset{.}{\psi} \cdot \left( {{{l \cdot \cos}\;\delta_{RR}} + {{b \cdot \sin}\;\delta_{RR}}} \right)}{v_{FL} \cdot {\sin\left( {\delta_{RR} - \delta_{FL}} \right)}}}},{k_{RL} = {{\frac{{b \cdot \overset{.}{\psi}} + {\cos\;{\delta_{FR} \cdot \frac{\overset{.}{\psi}\left( {{{l \cdot \cos}\;\delta_{RL}} + {{b \cdot \sin}\;\delta_{RL}}} \right)}{\sin\left( {\delta_{FR} - \delta_{RL}} \right)}}}}{{v_{RL} \cdot \cos}\;\delta_{RL}}\mspace{14mu}{with}\mspace{14mu} k_{FR}} = \frac{\overset{.}{\psi} \cdot \left( {{{l \cdot \cos}\;\delta_{RL}} + {{b \cdot \sin}\;\delta_{RL}}} \right)}{v_{FR} \cdot {\sin\left( {\delta_{FR} - \delta_{RL}} \right)}}}},$ where δ_(RL) Wheel steering angle rear left δ_(RR) Wheel steering angle rear right.
 18. The method of claim 13 wherein the following measured values are input in the calculation of the correction factors: the measured yaw rate and the wheel steering angles of the steerable wheels.
 19. The method of claim 13 wherein the correction factors are determined only when the measured yaw rate is >0.05°/s.
 20. The method of claim 13 wherein the correction factors are determined only when the measured yaw acceleration is <0.01°/s².
 21. The method of claim 13 wherein the correction factors are determined only when the wheel speed is >0.2 m/s.
 22. The method of claim 13 wherein the correction factors are determined only if the wheel acceleration is <0.1 m/s².
 23. A device which is configured to carry out the method of claim
 13. 24. A steer-by-wire steering system for a motor vehicle comprising the device of claim
 23. 